measuring risk in investments
DESCRIPTION
Measuring risk in investmentsTRANSCRIPT
1
Picking the Right Projects: Investment Analysis
2
First Principles
Invest in projects that yield a return greater than the minimum acceptable hurdle rate.– The hurdle rate should be higher for riskier projects and reflect the
financing mix used - owners’ funds (equity) or borrowed money (debt)
– Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects.
Choose a financing mix that minimizes the hurdle rate and matches the assets being financed.
If there are not enough investments that earn the hurdle rate, return the cash to stockholders.– The form of returns - dividends and stock buybacks - will depend upon
the stockholders’ characteristics.
3
What is a investment or a project?
Any decision that requires the use of resources (financial or otherwise) is a project.
Broad strategic decisions– Entering new areas of business– Entering new markets– Acquiring other companies
Tactical decisions Management decisions
– The product mix to carry– The level of inventory and credit terms
Decisions on delivering a needed service– Lease or buy a distribution system– Creating and delivering a management information system
4
The notion of a benchmark
Since financial resources are finite, there is a hurdle that projects have to cross before being deemed acceptable.
This hurdle will be higher for riskier projects than for safer projects. A simple representation of the hurdle rate is as follows:
Hurdle rate = Riskless Rate + Risk Premium The two basic questions that every risk and return model in finance
tries to answer are:– How do you measure risk?
– How do you translate this risk measure into a risk premium?
5
What is Risk?
Risk, in traditional terms, is viewed as a ‘negative’. Webster’s dictionary, for instance, defines risk as “exposing to danger or hazard”. The Chinese symbols for risk, reproduced below, give a much better description of risk
The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity.
6
The Capital Asset Pricing Model
Uses variance as a measure of risk Specifies that a portion of variance can be diversified away, and that is
only the non-diversifiable portion that is rewarded. Measures the non-diversifiable risk with beta, which is standardized
around one. Translates beta into expected return -
Expected Return = Riskfree rate + Beta * Risk Premium Works as well as the next best alternative in most cases.
7
The Mean-Variance Framework
The variance on any investment measures the disparity between actual and expected returns.
Expected Return
Low Variance Investment
High Variance Investment
8
The Importance of Diversification: Risk Types
The risk (variance) on any individual investment can be broken down into two sources. Some of the risk is specific to the firm, and is called firm-specific, whereas the rest of the risk is market wide and affects all investments.
The risk faced by a firm can be fall into the following categories –– (1) Project-specific; an individual project may have higher or lower cash
flows than expected. – (2) Competitive Risk, which is that the earnings and cash flows on a
project can be affected by the actions of competitors. – (3) Industry-specific Risk, which covers factors that primarily impact the
earnings and cash flows of a specific industry. – (4) International Risk, arising from having some cash flows in currencies
other than the one in which the earnings are measured and stock is priced – (5) Market risk, which reflects the effect on earnings and cash flows of
macro economic factors that essentially affect all companies
9
The Effects of Diversification
Firm-specific risk can be reduced, if not eliminated, by increasing the number of investments in your portfolio (i.e., by being diversified). Market-wide risk cannot. This can be justified on either economic or statistical grounds.
On economic grounds, diversifying and holding a larger portfolio eliminates firm-specific risk for two reasons-– (a) Each investment is a much smaller percentage of the portfolio, muting
the effect (positive or negative) on the overall portfolio.
– (b) Firm-specific actions can be either positive or negative. In a large portfolio, it is argued, these effects will average out to zero. (For every firm, where something bad happens, there will be some other firm, where something good happens.)
10
The Role of the Marginal Investor
The marginal investor in a firm is the investor who is most likely to be the buyer or seller on the next trade.
Generally speaking, the marginal investor in a stock has to own a lot of stock and also trade a lot.
Since trading is required, the largest investor may not be the marginal investor, especially if he or she is a founder/manager of the firm (Michael Dell at Dell Computers or Bill Gates at Microsoft)
In all risk and return models in finance, we assume that the marginal investor is well diversified.
11
The Market Portfolio
Assuming diversification costs nothing (in terms of transactions costs), and that all assets can be traded, the limit of diversification is to hold a portfolio of every single asset in the economy (in proportion to market value). This portfolio is called the market portfolio.
Individual investors will adjust for risk, by adjusting their allocations to this market portfolio and a riskless asset (such as a T-Bill)
Preferred risk level Allocation decisionNo risk 100% in T-BillsSome risk 50% in T-Bills; 50% in Market Portfolio;A little more risk 25% in T-Bills; 75% in Market PortfolioEven more risk 100% in Market PortfolioA risk hog.. Borrow money; Invest in market portfolio; Every investor holds some combination of the risk free asset and the
market portfolio.
12
The Risk of an Individual Asset
The risk of any asset is the risk that it adds to the market portfolio Statistically, this risk can be measured by how much an asset moves
with the market (called the covariance) Beta is a standardized measure of this covariance Beta is a measure of the non-diversifiable risk for any asset can be
measured by the covariance of its returns with returns on a market index, which is defined to be the asset's beta.
The cost of equity will be the required return,
Cost of Equity = Rf + Equity Beta * (E(Rm) - Rf)
where,
Rf = Riskfree rate
E(Rm) = Expected Return on the Market Index
13
Limitations of the CAPM
1. The model makes unrealistic assumptions
2. The parameters of the model cannot be estimated precisely- Definition of a market index
- Firm may have changed during the 'estimation' period'
3. The model does not work well- If the model is right, there should be
a linear relationship between returns and betas
the only variable that should explain returns is betas
- The reality is that the relationship between betas and returns is weak
Other variables (size, price/book value) seem to explain differences in returns better.
14
Alternatives to the CAPM
The risk in an investment can be measured by the variance in actual returns around an expected returnE(R)Riskless InvestmentLow Risk InvestmentHigh Risk InvestmentE(R)E(R)Risk that is specific to investment (Firm Specific) Risk that affects all investments (Market Risk)Can be diversified away in a diversified portfolio Cannot be diversified away since most assets1. each investment is a small proportion of portfolio are affected by it.2. risk averages out across investments in portfolioThe marginal investor is assumed to hold a “diversified” portfolio. Thus, only market risk will be rewarded and priced.
The CAPMThe APMMulti-Factor ModelsProxy ModelsIf there is 1. no private information2. no transactions costthe optimal diversified portfolio includes everytraded asset. Everyonewill hold this market portfolioMarket Risk = Risk added by any investment to the market portfolio:
If there are no arbitrage opportunities then the market risk ofany asset must be captured by betas relative to factors that affect all investments.Market Risk = Risk exposures of any asset to market factors
Beta of asset relative toMarket portfolio (froma regression)
Betas of asset relativeto unspecified marketfactors (from a factoranalysis)
Since market risk affectsmost or all investments,it must come from macro economic factors.Market Risk = Risk exposures of any asset to macro economic factors.
Betas of assets relativeto specified macroeconomic factors (froma regression)
In an efficient market,differences in returnsacross long periods mustbe due to market riskdifferences. Looking forvariables correlated withreturns should then give us proxies for this risk.Market Risk = Captured by the Proxy Variable(s)
Equation relating returns to proxy variables (from aregression)
Step 1: Defining RiskStep 2: Differentiating between Rewarded and Unrewarded RiskStep 3: Measuring Market Risk
15
Identifying the Marginal Investor in your firm…
Percent of Stock held by
Institutions
Percent of Stock held by
Insiders
Marginal Investor
High Low Institutional Investora
High High Institutional Investor, with
insider influence
Low High (held by
founder/manager of firm)
Insider (often undiversified)
Low High (held by wealthy
individual investor)
Wealthy individual
investor, fairly diversified
Low Low Small individual investor
with restricted
diversification
16
Looking at Disney’s top stockholders (again)
17
Analyzing Disney’s Stockholders
Percent of stock held by insiders = 1% Percent of stock held by institutions = 62%
Who is the marginal investor in Disney?
18
Application Test: Who is the marginal investor in your firm?
You can get information on insider and institutional holdings in your firm from:
http://finance.yahoo.com/
Enter your company’s symbol and choose profile. Looking at the breakdown of stockholders in your firm, consider
whether the marginal investor isa) An institutional investor
b) An individual investor
c) An insider
19
Inputs required to use the CAPM -
(a) the current risk-free rate
(b) the expected market risk premium (the premium expected for investing in risky assets over the riskless asset)
(c) the beta of the asset being analyzed.
20
The Riskfree Rate and Time Horizon
On a riskfree asset, the actual return is equal to the expected return. Therefore, there is no variance around the expected return.
For an investment to be riskfree, i.e., to have an actual return be equal to the expected return, two conditions have to be met –– There has to be no default risk, which generally implies that the security
has to be issued by the government. Note, however, that not all governments can be viewed as default free.
– There can be no uncertainty about reinvestment rates, which implies that it is a zero coupon security with the same maturity as the cash flow being analyzed.
21
Riskfree Rate in Practice
The riskfree rate is the rate on a zero coupon government bond matching the time horizon of the cash flow being analyzed.
Theoretically, this translates into using different riskfree rates for each cash flow - the 1 year zero coupon rate for the cash flow in year 1, the 2-year zero coupon rate for the cash flow in year 2 ...
Practically speaking, if there is substantial uncertainty about expected cash flows, the present value effect of using time varying riskfree rates is small enough that it may not be worth it.
22
The Bottom Line on Riskfree Rates
Using a long term government rate (even on a coupon bond) as the riskfree rate on all of the cash flows in a long term analysis will yield a close approximation of the true value.
For short term analysis, it is entirely appropriate to use a short term government security rate as the riskfree rate.
If the analysis is being done in real terms (rather than nominal terms) use a real riskfree rate, which can be obtained in one of two ways –– from an inflation-indexed government bond, if one exists
– set equal, approximately, to the long term real growth rate of the economy in which the valuation is being done.
Data Source: You can get riskfree rates for the US in a number of sites. Try http://www.bloomberg.com/markets.
23
Measurement of the risk premium
The risk premium is the premium that investors demand for investing in an average risk investment, relative to the riskfree rate.
As a general proposition, this premium should be– greater than zero
– increase with the risk aversion of the investors in that market
– increase with the riskiness of the “average” risk investment
24
What is your risk premium?
Assume that stocks are the only risky assets and that you are offered two investment options:
– a riskless investment (say a Government Security), on which you can make 5%
– a mutual fund of all stocks, on which the returns are uncertain
How much of an expected return would you demand to shift your money from the riskless asset to the mutual fund?
a) Less than 5%
b) Between 5 - 7%
c) Between 7 - 9%
d) Between 9 - 11%
e) Between 11- 13%
f) More than 13%
Check your premium against the survey premium on my web site.
25
Risk Aversion and Risk Premiums
If this were the capital market line, the risk premium would be a weighted average of the risk premiums demanded by each and every investor.
The weights will be determined by the magnitude of wealth that each investor has. Thus, Warren Bufffet’s risk aversion counts more towards determining the “equilibrium” premium than yours’ and mine.
As investors become more risk averse, you would expect the “equilibrium” premium to increase.
26
Risk Premiums do change..
Go back to the previous example. Assume now that you are making the same choice but that you are making it in the aftermath of a stock market crash (it has dropped 25% in the last month). Would you change your answer?a) I would demand a larger premium
b) I would demand a smaller premium
c) I would demand the same premium
27
Estimating Risk Premiums in Practice
Survey investors on their desired risk premiums and use the average premium from these surveys.
Assume that the actual premium delivered over long time periods is equal to the expected premium - i.e., use historical data
Estimate the implied premium in today’s asset prices.
28
The Survey Approach
Surveying all investors in a market place is impractical. However, you can survey a few investors (especially the larger
investors) and use these results. In practice, this translates into surveys of money managers’ expectations of expected returns on stocks over the next year.
The limitations of this approach are:– there are no constraints on reasonability (the survey could produce
negative risk premiums or risk premiums of 50%)
– they are extremely volatile
– they tend to be short term; even the longest surveys do not go beyond one year
29
The Historical Premium Approach
This is the default approach used by most to arrive at the premium to use in the model
In most cases, this approach does the following– it defines a time period for the estimation (1926-Present, 1962-Present....)
– it calculates average returns on a stock index during the period– it calculates average returns on a riskless security over the period
– it calculates the difference between the two– and uses it as a premium looking forward
The limitations of this approach are:– it assumes that the risk aversion of investors has not changed in a
systematic way across time. (The risk aversion may change from year to year, but it reverts back to historical averages)
– it assumes that the riskiness of the “risky” portfolio (stock index) has not changed in a systematic way across time.
30
Historical Average Premiums for the United States
Arithmetic average Geometric AverageStocks - Stocks - Stocks - Stocks -
Historical Period T.Bills T.Bonds T.Bills T.Bonds1928-2003 7.92% 6.54% 5.99% 4.82%1963-2003 6.09% 4.70% 4.85% 3.82%1993-2003 8.43% 4.87% 6.68% 3.57%What is the right premium? Go back as far as you can. Otherwise, the standard error in the estimate will be large. (
Be consistent in your use of a riskfree rate. Use arithmetic premiums for one-year estimates of costs of equity and geometric
premiums for estimates of long term costs of equity.Data Source: Check out the returns by year and estimate your own historical premiums by
going to updated data on my web site.
€
Std Error in estimate = Annualized Std deviation in Stock prices
Number of years of historical data)
31
What about historical premiums for other markets?
Historical data for markets outside the United States is available for much shorter time periods. The problem is even greater in emerging markets.
The historical premiums that emerge from this data reflects this and there is much greater error associated with the estimates of the premiums.
32
One solution: Look at a country’s bond rating and default spreads as a start
Ratings agencies such as S&P and Moody’s assign ratings to countries that reflect their assessment of the default risk of these countries. These ratings reflect the political and economic stability of these countries and thus provide a useful measure of country risk. In September 2003, for instance, Brazil had a country rating of B2.
If a country issues bonds denominated in a different currency (say dollars or euros), you can also see how the bond market views the risk in that country. In September 2003, Brazil had dollar denominated C-Bonds, trading at an interest rate of 10.17%. The US treasury bond rate that day was 4.16%, yielding a default spread of 6.01% for Brazil.
Many analysts add this default spread to the US risk premium to come up with a risk premium for a country. Using this approach would yield a risk premium of 10.83% for Brazil, if we use 4.82% as the premium for the US.
33
Beyond the default spread
Country ratings measure default risk. While default risk premiums and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads. If we can compute how much more risky the equity market is, relative to the bond market, we could use this information. For example,– Standard Deviation in Bovespa (Equity) = 33.37%
– Standard Deviation in Brazil C-Bond = 26.15%
– Default spread on C-Bond = 6.01%
– Country Risk Premium for Brazil = 6.01% (33.37%/26.15%) = 7.67%% Note that this is on top of the premium you estimate for a mature
market. Thus, if you assume that the risk premium in the US is 4.82%, the risk premium for Brazil would be 12.49%.
34
Implied Equity Premiums
We can use the information in stock prices to back out how risk averse the market is and how much of a risk premium it is demanding.
If you pay the current level of the index, you can expect to make a return of 7.94% on stocks (which is obtained by solving for r in the following equation)
Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 7.94% - 4.25% = 3.69%
January 1, 2004S&P 500 is at 1111.91In 2003, dividends & stock buybacks were 2.81% of the index, generating 31.29 in cashflows
Analysts expect earnings to grow 9.5% a year for the next 5 years as the economy comes out of a recession.After year 5, we will assume that earnings on the index will grow at 4.25%, the same rate as the entire economy
34.2637.5241.0844.9849.26
€
1111.91 =34.26
(1+ r)+
37.52
(1+ r)2+
41.08
(1+ r)3+
44.98
(1+ r)4+
49.26
(1+ r)5+
49.26(1.0425)
(r − .0425)(1+ r)5
35
Implied Premiums in the US
36
Application Test: A Market Risk Premium
Based upon our discussion of historical risk premiums so far, the risk premium looking forward should be:
About 7.92%, which is what the arithmetic average premium has been since 1928, for stocks over T.Bills
About 4.82%, which is the geometric average premium since 1928, for stocks over T.Bonds
About 3.7%, which is the implied premium in the stock market today
37
Estimating Beta
The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) -
Rj = a + b Rm
– where a is the intercept and b is the slope of the regression. The slope of the regression corresponds to the beta of the stock, and
measures the riskiness of the stock.
38
Estimating Performance
The intercept of the regression provides a simple measure of performance during the period of the regression, relative to the capital asset pricing model. Rj = Rf + b (Rm - Rf)
= Rf (1-b) + b Rm ........... Capital Asset Pricing Model
Rj = a + b Rm ........... Regression Equation
If
a > Rf (1-b) .... Stock did better than expected during regression period
a = Rf (1-b) .... Stock did as well as expected during regression period
a < Rf (1-b) .... Stock did worse than expected during regression period
This is Jensen's alpha.
39
Firm Specific and Market Risk
The R squared (R2) of the regression provides an estimate of the proportion of the risk (variance) of a firm that can be attributed to market risk;
The balance (1 - R2) can be attributed to firm specific risk.
40
Setting up for the Estimation
Decide on an estimation period– Services use periods ranging from 2 to 5 years for the regression
– Longer estimation period provides more data, but firms change.
– Shorter periods can be affected more easily by significant firm-specific event that occurred during the period (Example: ITT for 1995-1997)
Decide on a return interval - daily, weekly, monthly– Shorter intervals yield more observations, but suffer from more noise.
– Noise is created by stocks not trading and biases all betas towards one. Estimate returns (including dividends) on stock
– Return = (PriceEnd - PriceBeginning + DividendsPeriod)/ PriceBeginning
– Included dividends only in ex-dividend month Choose a market index, and estimate returns (inclusive of dividends)
on the index for each interval for the period.
41
Choosing the Parameters: Disney
Period used: 5 years Return Interval = Monthly Market Index: S&P 500 Index. For instance, to calculate returns on Disney in April 1992,
– Price for Disney at end of March = $ 37.87
– Price for Disney at end of April = $ 36.42
– Dividends during month = $0.05 (It was an ex-dividend month)
– Return =($36.42 - $ 37.87 + $ 0.05)/$ 37.87=-3.69% To estimate returns on the index in the same month
– Index level (including dividends) at end of March = 404.35
– Index level (including dividends) at end of April = 415.53
– Return =(415.53 - 404.35)/ 404.35 = 2.76%
42
Disney’s Historical Beta
Disney versus S&P 500: 1992-1996
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
-15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00%
43
The Regression Output
ReturnsDisney = -0.01% + 1.40 ReturnsS & P 500 (R squared=32.41%)
(0.27) Intercept = -0.01% Slope = 1.40
44
Analyzing Disney’s Performance
Intercept = -0.01%– This is an intercept based on monthly returns. Thus, it has to be compared
to a monthly riskfree rate.
– Between 1992 and 1996, Monthly Riskfree Rate = 0.4% (Annual T.Bill rate divided by 12) Riskfree Rate (1-Beta) = 0.4% (1-1.40) = -.16%
The Comparison is then betweenIntercept versus Riskfree Rate (1 - Beta)
-0.01% versus 0.4%(1-1.40)=-0.16%
– Jensen’s Alpha = -0.01% -(-0.16%) = 0.15% Disney did 0.15% better than expected, per month, between 1992 and
1996.– Annualized, Disney’s annual excess return = (1.0015)12-1= 1.81%
45
More on Jensen’s Alpha
If you did this analysis on every stock listed on an exchange, what would the average Jensen’s alpha be across all stocks?a) Depend upon whether the market went up or down during the period
b) Should be zero
c) Should be greater than zero, because stocks tend to go up more often than down
46
Estimating Disney’s Beta
Slope of the Regression of 1.40 is the beta Regression parameters are always estimated with noise. The noise is
captured in the standard error of the beta estimate, which in the case of Disney is 0.27.
Assume that I asked you what Disney’s true beta is, after this regression. – What is your best point estimate?
– What range would you give me, with 67% confidence?
– What range would you give me, with 95% confidence?
47
The Dirty Secret of “Standard Error”
Distribution of Standard Errors: Beta Estimates for U.S. stocks
0
200
400
600
800
1000
1200
1400
1600
<.10 .10 - .20 .20 - .30 .30 - .40 .40 -.50 .50 - .75 > .75
Standard Error in Beta Estimate
Nu
mb
er
of
Fir
ms
48
Breaking down Disney’s Risk
R Squared = 32% This implies that
– 32% of the risk at Disney comes from market sources
– 68%, therefore, comes from firm-specific sources The firm-specific risk is diversifiable and will not be rewarded
49
The Relevance of R Squared
You are a diversified investor trying to decide whether you should invest in Disney or Amgen. They both have betas of 140, but Disney has an R Squared of 32% while Amgen’s R squared of only 15%. Which one would you invest in?a) Amgen, because it has the lower R squared
b) Disney, because it has the higher R squared
c) You would be indifferent
Would your answer be different if you were an undiversified investor?
50
Beta Estimation in Practice: Bloomberg
51
Estimating Expected Returns: September 30, 1997
Inputs to the expected return calculation– Disney’s Beta = 1.40
– Riskfree Rate = 7.00% (Long term Government Bond rate)
– Risk Premium = 5.50% (Approximate historical premium) Expected Return = Riskfree Rate + Beta (Risk Premium)
= 7.00% + 1.40 (5.50%) = 14.70%
52
Use to a Potential Investor in Disney
As a potential investor in Disney, what does this expected return of 14.70% tell you?a) This is the return that I can expect to make in the long term on Disney, if
the stock is correctly priced and the CAPM is the right model for risk,
b) This is the return that I need to make on Disney in the long term to break even on my investment in the stock
c) Both
Assume now that you are an active investor and that your research suggests that an investment in Disney will yield 25% a year for the next 5 years. Based upon the expected return of 14.70%, you woulda) Buy the stock
b) Sell the stock
53
How managers use this expected return
Managers at Disney– need to make at least 14.70% as a return for their equity investors to break
even.
– this is the hurdle rate for projects, when the investment is analyzed from an equity standpoint
In other words, Disney’s cost of equity is 14.70%. What is the cost of not delivering this cost of equity?
54
Application Test: Analyzing the Risk Regression
Using your Bloomberg risk and return print out, answer the following questions:– How well or badly did your stock do, relative to the market, during the
period of the regression? (You can assume an annualized riskfree rate of 4.8% during the regression period)
Intercept - 0.4% (1- Beta) = Jensen’s Alpha
– What proportion of the risk in your stock is attributable to the market? What proportion is firm-specific?
– What is the historical estimate of beta for your stock? What is the range on this estimate with 67% probability? With 95% probability?
– Based upon this beta, what is your estimate of the required return on this stock?
Riskless Rate + Beta * Risk Premium
55
A Quick Test
You are advising a very risky software firm on the right cost of equity to use in project analysis. You estimate a beta of 2.0 for the firm and come up with a cost of equity of 18%. The CFO of the firm is concerned about the high cost of equity and wants to know whether there is anything he can do to lower his beta.
How do you bring your beta down?
Should you focus your attention on bringing your beta down? a) Yes
b) No
56
Disney’s Beta Calculation: An Update from 2002
Jensen’s alpha = -0.39% - 0.30 (1 - 0.94) = -0.41%Annualized = (1-.0041)^12-1 = -4.79%
57
Aracruz’s Beta?
58
Telebras: High R Squared?
59
A Few Questions
The R squared for Telebras is very high (70%), at least relative to U.S. firms. Why is that?
The beta for Telebras is 1.11. – Is this an appropriate measure of risk?
– If not, why not? The beta for every other stock in the index is also misestimated. Is
there a way to get a better estimate?
60
Try different indices?
The Local Solution: Estimate the beta relative to a local index, that is equally weighted or more diverse than the one in use.
The U.S. Solution: If the stock has an ADR listed on the U.S. exchanges, estimate the beta relative to the S&P 500.
The Global Solution: Use a global index to estimate the beta For Aracruz,
Index BetaStandard Error
Brazil I-Senn 0.69 0.18
S & P 500 (with ADR) 0.46 0.30
Morgan Stanley Capital Index (with ADR)0.35 0.32 As your index gets broader, your standard error gets larger.
61
Beta: Exploring Fundamentals
Beta = 1Beta > 1Beta = 0Beta < 1Real Networks: 3.24Qwest Communications: 2.60General Electric: 1.10Microsoft: 1..25Philip Morris: 0.65Exxon Mobil: 0.40Harmony Gold Mining: - 0.10Enron: 0.95
62
Determinant 1: Product Type
Industry Effects: The beta value for a firm depends upon the sensitivity of the demand for its products and services and of its costs to macroeconomic factors that affect the overall market. – Cyclical companies have higher betas than non-cyclical firms
– Firms which sell more discretionary products will have higher betas than firms that sell less discretionary products
63
A Simple Test
Consider an investment in Tiffany’s. What kind of beta do you think this investment will have?a) Much higher than one
b) Close to one
c) Much lower than one
64
Determinant 2: Operating Leverage Effects
Operating leverage refers to the proportion of the total costs of the firm that are fixed.
Other things remaining equal, higher operating leverage results in greater earnings variability which in turn results in higher betas.
65
Measures of Operating Leverage
Fixed Costs Measure = Fixed Costs / Variable Costs This measures the relationship between fixed and variable costs. The
higher the proportion, the higher the operating leverage.
EBIT Variability Measure = % Change in EBIT / % Change in Revenues This measures how quickly the earnings before interest and taxes
changes as revenue changes. The higher this number, the greater the operating leverage.
66
A Look at Disney’s Operating Leverage
Year Net Sales % Change
in Sales
EBIT % Change
in EBIT
1987 2877 756
1988 3438 19.50% 848 12.17%
1989 4594 33.62% 1177 38.80%
1990 5844 27.21% 1368 16.23%
1991 6182 5.78% 1124 -17.84%
1992 7504 21.38% 1429 27.14%
1993 8529 13.66% 1232 -13.79%
1994 10055 17.89% 1933 56.90%
1995 12112 20.46% 2295 18.73%
1996 18739 54.71% 2540 10.68%
Average 23.80% 16.56%
67
Reading Disney’s Operating Leverage
Operating Leverage = % Change in EBIT/ % Change in Sales
= 16.56% / 23.80 % = 0.70 This is lower than the operating leverage for other entertainment firms,
which we computed to be 1.15. This would suggest that Disney has lower fixed costs than its competitors.
The acquisition of Capital Cities by Disney in 1996 may be skewing the operating leverage downwards. For instance, looking at the operating leverage for 1987-1995:Operating Leverage1987-95 = 17.29%/19.94% = 0.87
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A Test
Assume that you are comparing a European automobile manufacturing firm with a U.S. automobile firm. European firms are generally much more constrained in terms of laying off employees, if they get into financial trouble. What implications does this have for betas, if they are estimated relative to a common index?a) European firms will have much higher betas than U.S. firms
b) European firms will have similar betas to U.S. firms
c) European firms will have much lower betas than U.S. firms
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Determinant 3: Financial Leverage
As firms borrow, they create fixed costs (interest payments) that make their earnings to equity investors more volatile.
This increased earnings volatility which increases the equity beta
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Equity Betas and Leverage
The beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio
L = u (1+ ((1-t)D/E))
whereL = Levered or Equity Beta
u = Unlevered Beta
t = Corporate marginal tax rate
D = Market Value of Debt
E = Market Value of Equity
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Effects of leverage on betas: Disney
The regression beta for Disney is 1.40. This beta is a levered beta (because it is based on stock prices, which reflect leverage) and the leverage implicit in the beta estimate is the average market debt equity ratio during the period of the regression (1992 to 1996)
The average debt equity ratio during this period was 14%. The unlevered beta for Disney can then be estimated:(using a marginal
tax rate of 36%)= Current Beta / (1 + (1 - tax rate) (Average Debt/Equity))
= 1.40 / ( 1 + (1 - 0.36) (0.14)) = 1.28
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Disney : Beta and Leverage
Debt to Capital Debt/Equity Ratio Beta Effect of Leverage
0.00% 0.00% 1.28 0.00
10.00% 11.11% 1.38 0.09
20.00% 25.00% 1.49 0.21
30.00% 42.86% 1.64 0.35
40.00% 66.67% 1.83 0.55
50.00% 100.00% 2.11 0.82
60.00% 150.00% 2.52 1.23
70.00% 233.33% 3.20 1.92
80.00% 400.00% 4.57 3.29
90.00% 900.00% 8.69 7.40
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Betas are weighted Averages
The beta of a portfolio is always the market-value weighted average of the betas of the individual investments in that portfolio.
Thus,– the beta of a mutual fund is the weighted average of the betas of the
stocks and other investment in that portfolio
– the beta of a firm after a merger is the market-value weighted average of the betas of the companies involved in the merger.
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The Disney/Cap Cities Merger: Pre-Merger
Disney: Beta = 1.15 Debt = $ 3,186 million Equity = $ 31,100 million Firm = $34,286
D/E = 0.10
ABC: Beta = 0.95 Debt = $ 615 million Equity = $ 18,500 million Firm= $ 19,115 D/E = 0.03
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Disney Cap Cities Beta Estimation: Step 1
Calculate the unlevered betas for both firms– Disney’s unlevered beta = 1.15/(1+0.64*0.10) = 1.08
– Cap Cities unlevered beta = 0.95/(1+0.64*0.03) = 0.93 Calculate the unlevered beta for the combined firm
– Unlevered Beta for combined firm
= 1.08 (34286/53401) + 0.93 (19115/53401)
= 1.026
[Remember to calculate the weights using the firm values of the two firms]
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Disney Cap Cities Beta Estimation: Step 2
If Disney had used all equity to buy Cap Cities– Debt = $ 615 + $ 3,186 = $ 3,801 million
– Equity = $ 18,500 + $ 31,100 = $ 49,600
– D/E Ratio = 3,801/49600 = 7.66%
– New Beta = 1.026 (1 + 0.64 (.0766)) = 1.08 Since Disney borrowed $ 10 billion to buy Cap Cities/ABC
– Debt = $ 615 + $ 3,186 + $ 10,000 = $ 13,801 million
– Equity = $ 39,600
– D/E Ratio = 13,801/39600 = 34.82%
– New Beta = 1.026 (1 + 0.64 (.3482)) = 1.25
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Firm Betas versus divisional Betas
Firm Betas as weighted averages: The beta of a firm is the weighted average of the betas of its individual projects.
At a broader level of aggregation, the beta of a firm is the weighted average of the betas of its individual division.
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Bottom-up versus Top-down Beta
The top-down beta for a firm comes from a regression The bottom up beta can be estimated by doing the following:
– Find out the businesses that a firm operates in– Find the unlevered betas of other firms in these businesses– Take a weighted (by sales or operating income) average of these
unlevered betas– Lever up using the firm’s debt/equity ratio
The bottom up beta will give you a better estimate of the true beta when– the standard error of the beta from the regression is high (and) the beta for
a firm is very different from the average for the business– the firm has reorganized or restructured itself substantially during the
period of the regression– when a firm is not traded
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Decomposing Disney’s Beta in 1997
Business Unlevered D/E Ratio Levered Riskfree Risk Cost of
Beta Beta Rate Premium Equity
Creative Content 1.25 20.92% 1.42 7.00% 5.50% 14.80%
Retailing 1.50 20.92% 1.70 7.00% 5.50% 16.35%
Broadcasting 0.90 20.92% 1.02 7.00% 5.50% 12.61%
Theme Parks 1.10 20.92% 1.26 7.00% 5.50% 13.91%
Real Estate 0.70 59.27% 0.92 7.00% 5.50% 12.31%
Disney 1.09 21.97% 1.25 7.00% 5.50% 13.85%
Business Estimated ValueComparable Firms Unlevered BetaDivision WeightCreative Content 22,167$ Motion Picture and TV program producers 1.25 35.71%Retailing 2,217$ High End Specialty Retailers 1.5 3.57%Broadcasting 18,842$ TV Broadcasting companies 0.9 30.36%Theme Parks 16,625$ Theme Park and Entertainment Complexes 1.1 26.79%Real Estate 2,217$ REITs specializing in hotel and vacation propertiers 0.7 3.57%Firm 62,068$ 100.00%
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Discussion Issue
If you were the chief financial officer of Disney, what cost of equity would you use in capital budgeting in the different divisions?a) The cost of equity for Disney as a company
b) The cost of equity for each of Disney’s divisions?
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Estimating Aracruz’s Bottom Up Beta
Comparable Firms Beta D/E Ratio Unlevered beta
Latin American Paper & Pulp (5) 0.70 65.00% 0.49
U.S. Paper and Pulp (45) 0.85 35.00% 0.69
Global Paper & Pulp (187) 0.80 50.00% 0.61 Aracruz has a cash balance which was 20% of the market value in 1997,
much higher than the typical cash balance at other paper firms
Unlevered Beta for Aracruz = (0.8) ( 0.61) + 0.2 (0) = 0.488 Using Aracruz’s gross D/E ratio of 66.67% & a tax rate of 33%:
Levered Beta for Aracruz = 0.49 (1+ (1-.33) (.6667)) = 0.71 Real Cost of Equity for Aracruz = 5% + 0.71 (7.5%) = 10.33%
Real Riskfree Rate = 5% (Long term Growth rate in Brazilian economy)
Risk Premium = 5.5% (US premium) + 2% (1996 Brazil default spread)
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Estimating Bottom-up Beta: Deutsche Bank
Deutsche Bank is in two different segments of business - commercial banking and investment banking.
To estimate its commercial banking beta, we will use the average beta of commercial banks in Germany.
To estimate the investment banking beta, we will use the average bet of investment banks in the U.S and U.K.
Comparable Firms Average Beta Weight
Commercial Banks in Germany 0.90 90%
U.K. and U.S. investment banks 1.30 10% Beta for Deutsche Bank = 0.9 (.90) + 0.1 (1.30)= 0.94 Cost of Equity for Deutsche Bank (in DM) = 7.5% + 0.94 (5.5%)
= 12.67%
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Estimating Betas for Non-Traded Assets
The conventional approaches of estimating betas from regressions do not work for assets that are not traded.
There are two ways in which betas can be estimated for non-traded assets– using comparable firms
– using accounting earnings
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Using comparable firms to estimate betas
Assume that you are trying to estimate the beta for a independent bookstore in New York City.
Company Name Beta D/E Ratio Market Cap $ (Mil )
Barnes & Noble 1.10 23.31% $ 1,416
Books-A-Million 1.30 44.35% $ 85
Borders Group 1.20 2.15% $ 1,706
Crown Books 0.80 3.03% $ 55
Average 1.10 18.21% $ 816 Unlevered Beta of comparable firms 1.10/(1 + (1-.36) (.1821)) = 0.99 If independent bookstore has similar leverage, beta = 1.10 If independent bookstore decides to use a debt/equity ratio of 25%:
Beta for bookstore = 0.99 (1+(1-..42)(.25)) = 1.13 (Tax rate used=42%)
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Using Accounting Earnings to Estimate Beta
Year S&P 500 Bookscape Year S&P 500 Bookscape
1980 -2.10% 3.55% 1989 2.60% 3.50%
1981 -6.70% 4.05% 1990 -18.00% -10.50%
1982 -45.50% -14.33% 1991 -47.40% -32.00%
1983 37.00% 47.55% 1992 64.50% 55.00%
1984 41.80% 65.00% 1993 20.00% 31.00%
1985 -11.80% 5.05% 1994 25.30% 21.06%
1986 7.00% 8.50% 1995 15.50% 11.55%
1987 41.50% 37.00% 1996 24.00% 19.88%
1988 41.80% 45.17%
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The Accounting Beta for Bookscape
Regressing the changes in profits at Bookscape against changes in profits for the S&P 500 yields the following:Bookscape Earnings Change = 0.09 + 0.80 (S & P 500 Earnings Change)
Based upon this regression, the beta for Bookscape’s equity is 0.80. Using operating earnings for both the firm and the S&P 500 should
yield the equivalent of an unlevered beta.
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Is Beta an Adequate Measure of Risk for a Private Firm?
The owners of most private firms are not diversified. Beta measures the risk added on to a diversified portfolio. Therefore, using beta to arrive at a cost of equity for a private firm willa) Under estimate the cost of equity for the private firm
b) Over estimate the cost of equity for the private firm
c) Could under or over estimate the cost of equity for the private firm
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Total Risk versus Market Risk
Adjust the beta to reflect total risk rather than market risk. This adjustment is a relatively simple one, since the R squared of the regression measures the proportion of the risk that is market risk. Total Beta = Market Beta / Correlation of the sector with the market
In the Bookscapes example, where the market beta is 1.10 and the average correlation of the comparable publicly traded firms is 33%,– Total Beta = 1.10/0.33 = 3.30
– Total Cost of Equity = 7% + 3.30 (5.5%)= 25.05%
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Application Test: Estimating a Bottom-up Beta
Based upon the business or businesses that your firm is in right now, and its current financial leverage, estimate the bottom-up unlevered beta for your firm.
Data Source: You can get a listing of unlevered betas by industry on my web site by going to updated data.
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From Cost of Equity to Cost of Capital
The cost of capital is a composite cost to the firm of raising financing to fund its projects.
In addition to equity, firms can raise capital from debt
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What is debt?
General Rule: Debt generally has the following characteristics:– Commitment to make fixed payments in the future
– The fixed payments are tax deductible
– Failure to make the payments can lead to either default or loss of control of the firm to the party to whom payments are due.
As a consequence, debt should include– Any interest-bearing liability, whether short term or long term.
– Any lease obligation, whether operating or capital.
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Estimating the Cost of Debt
If the firm has bonds outstanding, and the bonds are traded, the yield to maturity on a long-term, straight (no special features) bond can be used as the interest rate.
If the firm is rated, use the rating and a typical default spread on bonds with that rating to estimate the cost of debt.
If the firm is not rated, – and it has recently borrowed long term from a bank, use the interest rate
on the borrowing or
– estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt
The cost of debt has to be estimated in the same currency as the cost of equity and the cash flows in the valuation.
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Estimating Synthetic Ratings
The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio
Interest Coverage Ratio = EBIT / Interest Expenses For a firm, which has earnings before interest and taxes of $ 3,500
million and interest expenses of $ 700 million
Interest Coverage Ratio = 3,500/700= 5.00– Based upon the relationship between interest coverage ratios and ratings,
we would estimate a rating of A for the firm.
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Interest Coverage Ratios, Ratings and Default Spreads
If Interest Coverage Ratio is Estimated Bond Rating Default Spread> 8.50 AAA 0.75%6.50 - 8.50 AA 1.00%5.50 - 6.50 A+ 1.50%4.25 - 5.50 A 1.80%3.00 - 4.25 A– 2.00%2.50 - 3.00 BBB 2.25%2.00 - 2.50 BB 3.50%1.75 - 2.00 B+ 4.75%1.50 - 1.75 B 6.50%1.25 - 1.50 B – 8.00%0.80 - 1.25 CCC 10.00%0.65 - 0.80 CC 11.50%0.20 - 0.65 C 12.70%< 0.20 D 14.00%
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Application Test: Estimating a Cost of Debt
Based upon your firm’s current earnings before interest and taxes, its interest expenses, estimate– An interest coverage ratio for your firm
– A synthetic rating for your firm (use the table from previous page)
– A pre-tax cost of debt for your firm
– An after-tax cost of debt for your firm
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Estimating Market Value Weights
Market Value of Equity should include the following– Market Value of Shares outstanding
– Market Value of Warrants outstanding
– Market Value of Conversion Option in Convertible Bonds Market Value of Debt is more difficult to estimate because few firms
have only publicly traded debt. There are two solutions:– Assume book value of debt is equal to market value
– Estimate the market value of debt from the book value
– For Disney, with book value of $12,342 million, interest expenses of $479 million, a current cost of borrowing of 7.5% and an weighted average maturity of 3 years.
Estimated MV of Disney Debt = 479(1−
1(1.075)3
.075
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥+
12,342(1.075)3
=$11,180
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Converting Operating Leases to Debt
The “debt value” of operating leases is the present value of the lease payments, at a rate that reflects their risk.
In general, this rate will be close to or equal to the rate at which the company can borrow.
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Operating Leases at The Home Depot
The pre-tax cost of debt at the Home Depot is 6.25%Yr Operating Lease Expense Present Value 1 $ 294 $ 277 2 $ 291 $ 258 3 $ 264 $ 220 4 $ 245 $ 192 5 $ 236 $ 174 6-15 $ 270 $ 1,450 (PV of 10-yr annuity)
Present Value of Operating Leases =$ 2,571
Debt outstanding at the Home Depot = $1,205 + $2,571 = $3,776 mil(The Home Depot has other debt outstanding of $1,205 million)
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Application Test: Estimating Market Value
Estimate the – Market value of equity at your firm and Book Value of equity
– Market value of debt and book value of debt (If you cannot find the average maturity of your debt, use 3 years): Remember to capitalize the value of operating leases and add them on to both the book value and the market value of debt.
Estimate the– Weights for equity and debt based upon market value
– Weights for equity and debt based upon book value
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Current Cost of Capital: Disney
Equity– Cost of Equity = Riskfree rate + Beta * Risk Premium
= 7% + 1.25 (5.5%) = 13.85%
– Market Value of Equity = $50.88 Billion
– Equity/(Debt+Equity ) = 82% Debt
– After-tax Cost of debt =(Riskfree rate + Default Spread) (1-t)
= (7% +0.50) (1-.36) = 4.80%
– Market Value of Debt = $ 11.18 Billion
– Debt/(Debt +Equity) = 18% Cost of Capital = 13.85%(.82)+4.80%(.18) = 12.22%
50.88/(50.88+11.18)
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Disney’s Divisional Costs of Capital
Business E/(D+E) Cost of D/(D+E) After-tax Cost of Capital
Equity Cost of Debt
Creative Content 82.70% 14.80% 17.30% 4.80% 13.07%
Retailing 82.70% 16.35% 17.30% 4.80% 14.36%
Broadcasting 82.70% 12.61% 17.30% 4.80% 11.26%
Theme Parks 82.70% 13.91% 17.30% 4.80% 12.32%
Real Estate 62.79% 12.31% 37.21% 4.80% 9.52%
Disney 81.99% 13.85% 18.01% 4.80% 12.22%
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Application Test: Estimating Cost of Capital
Using the bottom-up unlevered beta that you computed for your firm, and the values of debt and equity you have estimated for your firm, estimate a bottom-up levered beta and cost of equity for your firm.
Based upon the costs of equity and debt that you have estimated, and the weights for each, estimate the cost of capital for your firm.
How different would your cost of capital have been, if you used book value weights?
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Choosing a Hurdle Rate
Either the cost of equity or the cost of capital can be used as a hurdle rate, depending upon whether the returns measured are to equity investors or to all claimholders on the firm (capital)
If returns are measured to equity investors, the appropriate hurdle rate is the cost of equity.
If returns are measured to capital (or the firm), the appropriate hurdle rate is the cost of capital.
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Back to First Principles
Invest in projects that yield a return greater than the minimum acceptable hurdle rate.– The hurdle rate should be higher for riskier projects and reflect the
financing mix used - owners’ funds (equity) or borrowed money (debt)
– Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects.
Choose a financing mix that minimizes the hurdle rate and matches the assets being financed.
If there are not enough investments that earn the hurdle rate, return the cash to stockholders.– The form of returns - dividends and stock buybacks - will depend upon
the stockholders’ characteristics.